Algebraic Geometry Seminar
Jack Huizenga
UIC
Effective divisors on the Hilbert scheme of points in the plane and interpolation for stable bundles
Abstract: The Hilbert scheme of n points in the projective plane parameterizes zero-dimensional subschemes of length n. An interesting problem is to describe the birational geometry of this space, and give modular interpretations for its various birational models. A first step in this program is to determine the cone of effective divisors on the Hilbert scheme.
We show the sections of many stable vector bundles satisfy a natural interpolation condition, and
that these bundles always give rise to the edge of the effective cone. To do this, we
give a generalization of Gaeta's theorem on the resolution of the ideal sheaf of a general collection of n
points in the plane. This resolution has a natural interpretation in terms of Bridgeland stability, and we observe that general ideal sheaves are always destabilized by exceptional bundles.
Wednesday December 5, 2012 at 4:00 PM in SEO 427